Russia's Duma lower house of parliament voted 446 in favour to none against for the amnesty, which commemorates 20 years since Russia ratified its current constitution.
The bill, branded as a mere token gesture by rights activists, went into effect later Wednesday and should also see several anti-Vladimir Putin protesters, jailed after a May 2012 rally, walk out of prison.
The amnesty affects a range of categories like mothers with dependents, minors and the elderly.
However, it also specifically mentions the charge of hooliganism as well as the charge of participating in mass riots.
The amendments meant that prosecution of the entire Greenpeace crew arrested after a protest in the Barents Sea and charged with hooliganism would end and the foreigners now staying in Saint Petersburg could finally go home.
The text of the amnesty bill, which does not require approval by the upper chamber of parliament, was published online and went into effect on Wednesday.
The 26 foreign crew from the Greenpeace Arctic Sunrise ship will request to leave, and still hope to be home by Christmas, said spokesman Ben Stewart.
"There is certainly a chance, but until they actually leave Russia, everything is speculation," he told AFP in an emailed comment.
The activists, who mounted a Gazprom drilling platform in the Arctic, were arrested on September 18th after the ship was boarded by Russian special forces.
They were first held under arrest in a jail in the northern city of Murmansk, where the ship remains under Russian control.
Last month, the entire crew was released on bail but Greenpeace said the foreigners were still not being allowed out of the country, with Russian investigators not giving migration officials a green light to issue exit visas.
“Greenpeace Switzerland rejoices for Marc Weber and his family,” the organization’s spokesman Yves Zenger told the ATS news agency after news of the amnesty.
The group said it hopes that he will be rapidly returned to Switzerland but it indicated that the activists still do not have the necessary documents to leave Russia.
The future of the Arctic Sunrise also remains a question mark, Greenpeace said.
Weber said the prospect of his freedom is no cause for joy.
“The Arctic is still threatened by the greed of oil companies,” he said in a comment released by Greenpeace.
“We will be able to rejoice only when the Arctic has been placed under protection.”
Meantime, the jailed members of Pussy Riot punk band, Nadezhda Tolokonnikova and Maria Alyokhina, who are serving two-year sentences on charges of hooliganism for staging an anti-Putin "punk prayer" protest in a cathedral, could be released as early as Thursday, Tolokonnikova's husband said.
The officials in Krasnoyarsk and Nizhny Novgorod, where the two women are currently held, have promised to free them "right away and without bureaucratic delay, probably tomorrow," Pyotr Verzilov wrote on his Twitter blog.
The duo's sentences run out in early March of next year.
'Not a wide amnesty'
The amnesty of mass rioting will also affect Russian protesters prosecuted under a probe after a rally on May 6, 2012, held in Moscow one day before Putin's inauguration for a third Kremlin term.
Three protesters who are under pre-trial arrest on charges of participation in mass riots will be freed.
The ruling United Russia party hailed the amnesty Wednesday as proof that Putin listens to the opposition and human rights activists.
United Russia party deputy Pavel Krasheninnikov, who presented the amnesty to the floor, told the Echo of Moscow radio that the amnesty will affect a total of about 15,000 people, and up to 3,500 people will be freed from jail.
However rights activists said the bill goes nowhere near far enough, with ex-tycoon turned Kremlin critic Mikhail Khodorkovsky not covered under the amnesty and even risking a third trial on new charges.
"This amnesty has nothing to do with what we proposed," said veteran rights defender Lyudmila Alexeyeva, noting that the number to be freed was tiny compared with Russia's total prison population of 700,000.